Problem: Jessica is 5 times as old as Vanessa. Eight years ago, Jessica was 9 times as old as Vanessa. How old is Vanessa now?
Explanation: We can use the given information to write down two equations that describe the ages of Jessica and Vanessa. Let Jessica's current age be $j$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $j = 5v$ Eight years ago, Jessica was $j - 8$ years old, and Vanessa was $v - 8$ years old. The information in the second sentence can be expressed in the following equation: $j - 8 = 9(v - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = 5v$ . Substituting this into our second equation, we get: $5v$ $-$ $8 = 9(v - 8)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $5 v - 8 = 9 v - 72$ Solving for $v$ , we get: $4 v = 64.$ $v = 16$.